# Magnetic poles and field problems

## Homework Statement

Draw this diagram:

Now do the following:
• find the unknown poles labelled with a question mark
• draw the magnetic field around the conductor shown
• determine the direction of the force acting on the conductor

## Homework Equations

Using the right-hand rule can help to solve for poles.

## The Attempt at a Solution

Did I do this correctly? Thanks in advance!

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I believe you got it correct. It's very easy even for someone with some expertise in this area to get a direction incorrect, but I believe you got it right. :)

kuruman
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You identified the poles correctly, but your magnetic field lines need improvement. Remember magnetic field lines form closed loops and should be perpendicular to the flat pole pieces. You show only one line and it's not closed in that the circulation is inconsistent.

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Additional item: You drew the magnetic field around the conductor from the current in the conductor correctly, but the magnetic field from the electromagnet will in general be much stronger.$\\$ [Edited note : As @David Lewis points out below in post 9, the magnetic field from the current in the conductor could be as large or larger than the magnetic field from the electromagnet. My previous statement is not accurate as it stands. It is sufficient to draw lines of flux that are not intended to show relative strengths]. $\\$ Also, as @kuruman pointed out, the lines of flux from the electromagnet that you show are somewhat incomplete. You might also want to label the north pole "+" and the south pole "-".

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What do you mean by 'the lines of flux'. Or which lines on the diagram are they? This is what my online textbook did as an example. Did I do it right and they are just teaching it strangely?

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What do you mean by 'the lines of flux'. Or which lines on the diagram are they? This is what my online textbook did as an example. Did I do it right and they are just teaching it strangely?

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I think you did reasonably well. It appears to be a somewhat introductory course, and what they asked for in regards to the magnetic field wasn't expressed very clearly. The magnetic flux lines from a horseshoe magnet are presented in the following "link" : https://www.nde-ed.org/EducationResources/CommunityCollege/MagParticle/Physics/MagneticFieldChar.htm Whether they were looking for these flux lines in their entirety is open for debate. Ideally, they would ask for this from the student, but it isn't completely clear whether this info was requested. $\\$ Additional item: They are teaching it somewhat strangely. (editing: In further consideration, what they are teaching works. It's not how I would solve it though. What they are doing sort of works from energy considerations, but the process as they are using it is in a very crude form.) $\\$ The force on a current carrying wire is $\vec{F}=(\vec{I} L) \times \vec{B}$. When I worked the problem, I determined the direction of the force by taking the vector cross product. The vector $\vec{B}$ here is simply that of the horseshoe magnet, and does not involve the magnetic field from the current in the wire. The magnetic field from the current in the wire is not needed to determine the direction of the force on the wire.

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The magnetic field from the current in the wire is not needed to determine the direction of the force on the wire.
Please explain. I thought force arises due to interaction between the magnetic field surrounding the wire, and the field of the permanent magnet.

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Please explain. I thought force arises due to interaction between the magnetic field surrounding the wire, and the field of the permanent magnet.
The current in the wire consists of moving electrical charges. These moving charges in the magnetic field experience a force $\vec{F}=Q \vec{v} \times \vec{B}$. This translates to $\vec{F}=(\vec{I} L) \times \vec{B}$ for the force on a current carrying wire of length $L$. $\\$ The approach this book seems to be using is using energy considerations, where energy density $U=C B^2$ for some constant $C$, and the force $\vec{F}=-\nabla E$ where the total energy of the magnetic fields of the system is $E=\int U \, d^3x$, and the total energy $E$ will be a function of the location of the current carrying wire. Doing it this way is a rather involved process. Trying to do this in a qualitative manner by saying like field lines repel, etc. is really, IMO, a rather crude and unreliable approach.

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Thank you. Those equations would come into play if you need to know how strong the force is.
You drew the magnetic field around the conductor from the current in the conductor correctly, but the magnetic field from the electromagnet will in general be much stronger.
The problem statement does not contain enough information to make that assumption.

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Thank you. Those equations would come into play if you need to know how strong the force is.
The problem statement does not contain enough information to make that assumption.
Agreed. Let me correct post 4 above. Thank you @David Lewis .

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Thanks guys, I think I will submit it like this.
Additional item: They are teaching it somewhat strangely. (editing: In further consideration, what they are teaching works. It's not how I would solve it though. What they are doing sort of works from energy considerations, but the process as they are using it is in a very crude form.)
Yes, I'm sure this is correct. It's really a pain. I am doing Functions with them as well and my Dad, who had been a calculus teacher for the past 20 years, said they teach Functions in a very strange way too.

You are asked to draw the magnetic field around the conductor. However, your drawing only needs to be accurate enough to answer the other two questions.

kuruman
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The magnetic flux lines from a horseshoe magnet are presented in the following "link" ...
The blurb at this link in the section General properties of Magnetic Lines of Force states that "They all have the same strength." For the life of me I cannot even guess what this can conceivably mean. Any ideas?

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The blurb at this link in the section General properties of Magnetic Lines of Force states that "They all have the same strength." For the life of me I cannot even guess what this can conceivably mean. Any ideas?
I think they are trying to quantify something in layman's terms, by saying when you draw flux lines for a single magnet, the density of lines is representative of the strength of the flux, and each line represents a specific amount of magnetic field strength. It's at a rather introductory level, but I think they did reasonably well in explaining it. $\\$ An additional item: Flux lines really can't be completely quantitative in a two dimensional drawing. To achieve the inverse square law effect along with $\nabla \cdot B=0$, etc. it really requires a 3-D drawing for them to work properly.

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kuruman
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I think they are trying to quantify something in layman's terms, by saying when you draw flux lines for a single magnet, the density of lines is representative of the strength of the flux, and each line represents a specific amount of magnetic field strength. It's at a rather introductory level, but I think they did reasonably well in explaining it.
Thank you. The very important idea of flux is conveyed indirectly. There is mention of "density" of lines but no statement that the field is weaker in regions of lower line density. Instead, the statement "They all have the same strength" can be misinterpreted to mean that if one moves along a field line, the strength (magnitude) of the field remains the same. I think your interpretation of what the author was trying to say is correct, but I don't think it was done effectively.

"They all have the same strength" can be misinterpreted to mean that if one moves along a field line, the strength (magnitude) of the field remains the same.
The strength of the magnetic field does not stay the same, but the magnitude of the force acting on test particles surrounding each field line does. When the lines are far apart, it takes more test particles to achieve the same amount of force.

kuruman
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The strength of the magnetic field does not stay the same, but the magnitude of the force acting on test particles surrounding each field line does. When the lines are far apart, it takes more test particles to achieve the same amount of force.
Unlike electric or gravitational field lines, magnetic field lines are not really lines of "force" as claimed in that the force is not locally tangent to the line. The test could be positive charges moving with unit velocity in which case the strength and direction of the magnetic field may be deduced from ω, q/m and the sense of the orbit. Not as simple to visualize as a positive test charge at the end of a spring of known k stretched to distance x, the direction of the stretch being the direction of the electric field.

Thank you. The very important idea of flux is conveyed indirectly. There is mention of "density" of lines but no statement that the field is weaker in regions of lower line density. Instead, the statement "They all have the same strength" can be misinterpreted to mean that if one moves along a field line, the strength (magnitude) of the field remains the same. I think your interpretation of what the author was trying to say is correct, but I don't think it was done effectively.
Strength of the field depends on no of relative density of field lines crossing through the point

I believe you got it correct. It's very easy even for someone with some expertise in this area to get a direction incorrect, but I believe you got it right. :)
I'm struggling with the same question and I don't get it. Doesn't the current flow out the positive end or the longer end of the battery and with the coil coiling around the right side of the magnet first, then the left side, shouldn't the poles be reversed because of the right-hand rule where when your thumb is pointing in the direction of the induced current, then the north pole is in the direction of your thumb?